The graph below, which uses Black-Scholes prices, describes the relation between time value of the EUROPEAN PUT option and the stock price. It assumes that: E = $60, T = 44 days, = 0.4, r = 6% (per year), and no dividends.

The at-the money option (with E=$60) has the highest time value.

a) Explain why the time value is falling more and more as we move from the stock price of $60 (which is equal to E) towards higher and higher stock prices. (3 points)

b) Explain why the time value is falling more and more as we move from the stock price of $60 (which is equal to E) towards lower and lower stock prices. (Hint: use the put-call parity to separate the options time value from its intrinsic value.) (3 points)

c) Using the assumptions in this question, explain why the time value becomes negative when the stock price falls below $50. (2 points)

Time value European put's time value as a function of stock price 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 30 50 60 70 80 90 Stock price 40